{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RCM4RXYF2CFG3Z66EEGH7XGEND","short_pith_number":"pith:RCM4RXYF","canonical_record":{"source":{"id":"1707.03129","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T05:00:53Z","cross_cats_sorted":[],"title_canon_sha256":"311520842d7b894767d215ded857c7d542c126f1005242d2212b929e7cada0c7","abstract_canon_sha256":"5c0dfa5b995a1565c980c57f7afb6849738863fee4af4e8e78985b374cd5ccd8"},"schema_version":"1.0"},"canonical_sha256":"8899c8df05d08a6de7de210c7fdcc468edab4fca04550dac784ab3b08efe86e3","source":{"kind":"arxiv","id":"1707.03129","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03129","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03129v3","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03129","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"RCM4RXYF2CFG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RCM4RXYF2CFG3Z66","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RCM4RXYF","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RCM4RXYF2CFG3Z66EEGH7XGEND","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03129","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T05:00:53Z","cross_cats_sorted":[],"title_canon_sha256":"311520842d7b894767d215ded857c7d542c126f1005242d2212b929e7cada0c7","abstract_canon_sha256":"5c0dfa5b995a1565c980c57f7afb6849738863fee4af4e8e78985b374cd5ccd8"},"schema_version":"1.0"},"canonical_sha256":"8899c8df05d08a6de7de210c7fdcc468edab4fca04550dac784ab3b08efe86e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:34.712649Z","signature_b64":"2L30y08N9i5rbpOdPTA/zY2yfd6sVChxr1ws6IYQUtP7wO2+g2kqYrg2pXizxBKyz/jg0qpLPGPX9OBrz/O2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8899c8df05d08a6de7de210c7fdcc468edab4fca04550dac784ab3b08efe86e3","last_reissued_at":"2026-05-17T23:55:34.712124Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:34.712124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03129","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fAiMkm6+X5dKEoj2MBnC78vH9QQYviZ7HY8/wbKqDcSg95RrxW7EiHqcj95WjArYKAnBqRZPQTdYEGmSiRGRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:47:44.600895Z"},"content_sha256":"c3f5eac695144f891fa7e80f992673d701a89f2c1bfb83a6d652aa4c38d3fdda","schema_version":"1.0","event_id":"sha256:c3f5eac695144f891fa7e80f992673d701a89f2c1bfb83a6d652aa4c38d3fdda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RCM4RXYF2CFG3Z66EEGH7XGEND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kurdyka-Lojasiewicz-Simon inequality for gradient flows in metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Australia (2) Universitat de Valencia, Daniel Hauer (1), Jos\\'e Mazon (2) ((1) University of Sydney, Spain), Valencia","submitted_at":"2017-07-11T05:00:53Z","abstract_excerpt":"This paper is dedicated to providing new tools and methods for studying the trend to equilibrium of gradient flows in metric spaces in the entropy and metric sense, to establish decay rates, finite time of extinction, and to characterize Lyapunov stable equilibrium points. In addition we outline that the celebrated Entropy-Entropy production inequality used in kinetic theory is nothing less than a global Kurdyka-Lojasiewicz-Simon inequality. This links two different areas, namely, algebraic geometry with kinetic theory. As an application of the tools developed in this paper, we obtain the foll"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03129","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMadNcgYPMcy6KuUabOSMpZBlJGHHi9/zTsfp7B+hd9yUTFZG1E5d2TxlFaIfQXipgbx0gvzVuxfs7ACUkMPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:47:44.601550Z"},"content_sha256":"8f742c3428e543de772e33454cb2b82fdd688935775ddb779d330022ac6b973d","schema_version":"1.0","event_id":"sha256:8f742c3428e543de772e33454cb2b82fdd688935775ddb779d330022ac6b973d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCM4RXYF2CFG3Z66EEGH7XGEND/bundle.json","state_url":"https://pith.science/pith/RCM4RXYF2CFG3Z66EEGH7XGEND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCM4RXYF2CFG3Z66EEGH7XGEND/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T04:47:44Z","links":{"resolver":"https://pith.science/pith/RCM4RXYF2CFG3Z66EEGH7XGEND","bundle":"https://pith.science/pith/RCM4RXYF2CFG3Z66EEGH7XGEND/bundle.json","state":"https://pith.science/pith/RCM4RXYF2CFG3Z66EEGH7XGEND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCM4RXYF2CFG3Z66EEGH7XGEND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RCM4RXYF2CFG3Z66EEGH7XGEND","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5c0dfa5b995a1565c980c57f7afb6849738863fee4af4e8e78985b374cd5ccd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T05:00:53Z","title_canon_sha256":"311520842d7b894767d215ded857c7d542c126f1005242d2212b929e7cada0c7"},"schema_version":"1.0","source":{"id":"1707.03129","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03129","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03129v3","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03129","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"RCM4RXYF2CFG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RCM4RXYF2CFG3Z66","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RCM4RXYF","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:8f742c3428e543de772e33454cb2b82fdd688935775ddb779d330022ac6b973d","target":"graph","created_at":"2026-05-17T23:55:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is dedicated to providing new tools and methods for studying the trend to equilibrium of gradient flows in metric spaces in the entropy and metric sense, to establish decay rates, finite time of extinction, and to characterize Lyapunov stable equilibrium points. In addition we outline that the celebrated Entropy-Entropy production inequality used in kinetic theory is nothing less than a global Kurdyka-Lojasiewicz-Simon inequality. This links two different areas, namely, algebraic geometry with kinetic theory. As an application of the tools developed in this paper, we obtain the foll","authors_text":"Australia (2) Universitat de Valencia, Daniel Hauer (1), Jos\\'e Mazon (2) ((1) University of Sydney, Spain), Valencia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T05:00:53Z","title":"Kurdyka-Lojasiewicz-Simon inequality for gradient flows in metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03129","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c3f5eac695144f891fa7e80f992673d701a89f2c1bfb83a6d652aa4c38d3fdda","target":"record","created_at":"2026-05-17T23:55:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5c0dfa5b995a1565c980c57f7afb6849738863fee4af4e8e78985b374cd5ccd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T05:00:53Z","title_canon_sha256":"311520842d7b894767d215ded857c7d542c126f1005242d2212b929e7cada0c7"},"schema_version":"1.0","source":{"id":"1707.03129","kind":"arxiv","version":3}},"canonical_sha256":"8899c8df05d08a6de7de210c7fdcc468edab4fca04550dac784ab3b08efe86e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8899c8df05d08a6de7de210c7fdcc468edab4fca04550dac784ab3b08efe86e3","first_computed_at":"2026-05-17T23:55:34.712124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:34.712124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2L30y08N9i5rbpOdPTA/zY2yfd6sVChxr1ws6IYQUtP7wO2+g2kqYrg2pXizxBKyz/jg0qpLPGPX9OBrz/O2Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:34.712649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03129","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3f5eac695144f891fa7e80f992673d701a89f2c1bfb83a6d652aa4c38d3fdda","sha256:8f742c3428e543de772e33454cb2b82fdd688935775ddb779d330022ac6b973d"],"state_sha256":"ecacb0e2da7594847390b2cc124d405d72e83237cfc193bb6cddb2172ca4070b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8+b0OhUxHw9x6+4y7777h3JmYmPrhkI2hb1oriZ8JWEMPVeFhjkQMkOcGIlbdza/Vkv2E+sWO4pjvysP3J9Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:47:44.604891Z","bundle_sha256":"368ddb447b04fd89b41709dd02be4cfe360d4e6dd455cd53e6f4dffb0f8156cd"}}